SAN FRANCISCO — Microsoft dangled a higher takeover bid in front of Yahoo on Friday, hoping to reach a friendly deal after a period of saber rattling.

The software maker upped its offer beyond the original value of $44.6 billion, or $31 per share, according to a person familiar with the matter. The specifics of the new offer weren’t known by this person, who didn’t want to be identified because the negotiations are still confidential.

The New York Times, citing unnamed sources, reported Microsoft boosted the offer by “by several dollars” per share.

Representatives from Microsoft and Yahoo declined to comment on the negotiations. The talks were expected to continue into the weekend.

In an intriguing twist, Microsoft Chairman Bill Gates and Yahoo President Susan Decker were both expected to be in Omaha, Neb., this weekend to attend Berkshire Hathaway’s annual meeting.

Both Gates and Decker are on the board of the company led by famed investor Warren Buffett.

The prospect of a sweetened offer lifted Yahoo shares 80 cents in extended trading after surging $1.86, or nearly 7 percent, to finish the regular session at $28.67.

Sunnyvale, Calif.-based Yahoo began pressing for a higher offer shortly after Microsoft made its unsolicited bid in February. That offer, which was made half in cash and half in stock, is currently valued at $42.3 billion, or $29.40 per share, reflecting the decline in Microsoft shares since it began its pursuit of the Internet pioneer.

Microsoft Chief Executive Steve Ballmer had held firm, insisting the original offer was fair in light of Yahoo’s eroding profits during the past two years. He threatened an attempt to oust Yahoo’s board if the 10 directors, including Chief Executive Jerry Yang, didn’t accept the offer by April 26.

Now that Yahoo has forced the issue by letting the deadline pass, Ballmer appears ready to put more money on the table.

In comments to Microsoft employees Thursday, Ballmer said he has a price in mind but didn’t reveal it.

“I know exactly what I think Yahoo is worth to me, exactly,” Ballmer told the employees, according to a transcript filed with the Securities and Exchange Commission. “I won’t go a dime above, and I will go to what I think it’s worth if that gets the deal done.”

Many analysts have predicted all along that Microsoft eventually would buy Yahoo $32 to $35 per share, so the news of Friday’s negotiations wasn’t a major surprise.

“It’s all going according to script,” said Ken Marlin, a New York investment banker specializing in technology deals.